Here is the process I used. I was lucky in the sense this car has a undercoating that was 99% intact and no rust repair was needed so it was mainly to remove dirt / grease and what looked like at some point someone painted parts of it with a black paint that dissolved easily with Mineral Spirts or gasoline and in some cases it may have been just dirt as it also, with some effort, came off with Fantastic cleaner.
Cleaning supplies used:
Green Scotch scrubbing pads.
Latex gloves for protection and eye protection.
Lacquer thinners for some stubborn spots.
Mineral Spirits for degrease.
tooth brush used to scrub nuts and bolts and small difficult areas.
Process:
1. Jack up car and put on jack stands so that I can move around under the car on a crawler.
2. Remove exhaust and heat shield, disconnect handbrake cables at two spots to drop them away from underside.
3. Remove fuel lines from car for detailed cleaning. Kept the brake line from front to back in place to avoid having to re do brake fluid.
4. remove old vapour line and replace with new. (on my car this runs from front of engine to plastic tank in trunk)
5. using scotch pad or tooth brush dipped in Mineral spirits working small areas at a time scrub underside then wipe away with a cloth or paper towels. This will take weeks to complete depending on your tolerance to working in this awkward position. I broke the task up into 1 foot x 1 foot sections. I generally try to clean i with the least harsh chemical which maybe just soap / dishwashing liquid. If that does not work then try the mineral spirits and if that don't work try lacquer thinner or some also suggested parafin. I tried gasoline too but the smell is terrible.
6. After this process is complete and if you want to you can paint the underside. (originally I was going to leave it natural but after seeing some cars painted I thought it looked good and as my car color is very close to what I think the undercoat was I went ahead and painted it in small sections at a time spraying it on in the flat areas and using a small paint brush to apply it in difficult areas like behind the springs and differential. The paint I used is high gloss which I think was a good choice. I thought that if I didn't like the gloss look I could always dull it with 0000 wool. But turns out I like the final results.
7. while the exhaust is out I cleaned and painted that in Satin look. Also cleaned the heat shield using the scotch pads and dish washing liquid.
8. Painted the clamps that helped the fuel / brake lines in gold paint. Cleaned all the lines and then re installed after the paint process is done.
I hope that helps. The only downside I can see in doing this is I am reluctant to to drive it as it looks too clean now.
Pinder